How to get absolute file path for linked texture image?
Not very nice, but it's working.

import os
import bpy

tex = bpy.data.images['WALL_1773.png']
# linked image from /project/assets/shaders/walls.blend

tex_path = tex.filepath
# '//../textures/walls/WALL_1773.png'

blend_dir_path = os.path.dirname(tex.library.filepath)
# '/project/assets/shaders'

full_path = blend_dir_path + tex_path[1:]
# '/project/assets/shaders/../textures/walls/WALL_1773.png'

norm_path = os.path.normpath(full_path)
# '/project/assets/textures/walls/WALL_1773.png'


Better code based on batFINGER's comment

import os
import bpy

tex = bpy.data.images['WALL_1773.png']
# linked image from /project/assets/shaders/walls.blend

full_path = bpy.path.abspath(tex.filepath, library=tex.library)
# '/project/assets/shaders/../textures/walls/WALL_1773.png'

norm_path = os.path.normpath(full_path)
# '/project/assets/textures/walls/WALL_1773.png'